Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies. (6th April 2015) - Nowak, Marian
Abstract : Let X be a completely regular Hausdorff space, and let( E, ‖ · ‖ E ) and( F, ‖ · ‖ F ) be Banach spaces. Let C b ( X, E ) be the space of all E -valued bounded, continuous functions defined on X, equipped with the strict topologies β z, where   z = σ, ∞, p, τ, t . General integral representation theorems of( β z, ‖ · ‖ F ) -continuous linear operators   T : C b ( X, E ) → F    with respect to the corresponding operator-valued measures are established. Strongly bounded and( β z, ‖ · ‖ F ) -continuous operators T : C b ( X, E ) → F are studied. We extend to "the completely regular setting" some classical results concerning operators on the spaces C ( X, E ) and C o ( X, E ), where X    is a compact or a locally compact space.